Herrera
et al. [1]} extended this novel idea
for time-dependent self-gravitating objects evolving in
\(\mathbb {Q}_{\mathbf {H}}\)  regime. In this case, the function
\(Y_{TF}\)  also contains the dissipative variables and for the
complete analysis of complexity, one must consider the simplest
evolution pattern described by the homologous condition. Later on,
Herrera et al. [2]} proposed the
complexity of a dissipative dynamical system evolving in the
\(\mathbb {Q}_{\mathbf {H}}\)  regime. In this case, they devised various
cosmological models under the condition of \(Y_{TF}=0\)  and the
\(\mathbb {Q}_{\mathbf {H}}\)  evolution. We are generalizing this study
by taking into consideration the \(f(\mathcal {G},\mathbf {T}^{2})\) 
corrections.
